WASHINGTON (CNN) -- Several administration officials and the House Republican Conference chairman said Friday that Attorney General Alberto Gonzales should step down, following the harsh response to his Senate testimony on last year's firing of eight U.S. attorneys.

Members of the Senate Judiciary Committee grilled Gonzales for hours Thursday about the dismissals.

Gonzales said more than 60 times that he "couldn't recall" certain incidents. His former chief of staff, Kyle Sampson, used that explanation 122 times during his testimony weeks ago.

Detractors say the Justice Department has not been straightforward about the reasons the attorneys were dismissed. The controversy has led to allegations of political interference with pending investigations.

"He did not distinguish himself in the hearing," said Rep. Adam Putnam, House GOP conference chairman. "There remains a cloud over the department."

"I think that they would be well-served by fresh leadership," said Putnam, who is often a spokesman for House Republicans. He said no one was doing "high fives" after the testimony.

During the hearings Thursday, while Democratic senators criticized Gonzales' leadership, some of the sharpest criticism came from Republicans on the Senate Judiciary Committee, including one who called for his resignation.

Sen. Tom Coburn, R-Oklahoma, said Gonzales should resign.

"The communication was atrocious. It was inconsistent -- it's generous to say that there were misstatements; it's a generous statement. And I believe you ought to suffer the consequences that these others have suffered," Coburn said, adding, "I believe the best way to put this behind us is your resignation." (Watch Coburn tell Gonzales he must "suffer the consequences")

"I think the attorney general ought to take the weekend and think about this and ask himself whether he can effectively reconstitute the attorney general's office," Sessions said, "and I'll be thinking about the same thing.

"If he feels like he cannot, then it would be best for the president and the country to resign."

Justice official: Gonzales 'feeling good'

According to a senior Justice Department official, Gonzales spoke to some senators Friday. The official would only say they included Sen. Arlen Specter, R-Pennsylvania, "and others" and was not sure whether he spoke to any Democrats. "The conversations went well," the official said but provided no details.

The official also said, "Attorney General Gonzales is in good spirits. He's optimistic, feeling good." "He is eager to get on with the other important work of the department," the official added.

The attorney general plans to participate in private and public events in the coming week in Washington.

After Gonzales' testimony Thursday, White House deputy press secretary Dana Perino said Gonzales has the full backing of the president:

"President Bush was pleased with the attorney general's testimony today. After hours of testimony in which he answered all of the senators' questions and provided thousands of pages of documents, he again showed that nothing improper occurred. He admitted the matter could have been handled much better, and he apologized for the disruption to the lives of the U.S. attorneys involved, as well as for the lack of clarity in his initial responses," Perino said.

White House insiders: Gonzales hurt himself

But White House insiders told CNN after the testimony that Gonzales hurt himself during his testimony.

The sources, involved in administration discussions about Gonzales, said two senior level White House aides who heard the testimony described Gonzales as "going down in flames," "not doing himself any favors," and "predictable."

And the administration officials who talked to CNN on Friday agreed that Gonzales' statements did little to help him regain credibility on Capitol Hill and, in fact, may have lost him the few supporters he had left.

One official, who works closely with Gonzales, described him as "out of touch" with the political pulse in Washington. The official said the attorney general is still optimistic that he can remedy the situation.

The White House sources acknowledge that no one knows what the president will do. No one is looking for a replacement yet, sources said, and the White House is waiting to see how this plays out with the public and members of Congress over the next couple of days.

"He and Al have to work this out ..." he said. "There is no indication that Gonzales thinks he needs to leave."

Former solicitor general mentioned as possible replacement

Several other officials said Republicans have begun discussing a possible replacement.

One name that consistently comes up is Ted Olson, former solicitor general. Olson is seen as having the experience, reputation and credibility needed to steer the department for the next year and a half, through the end of Bush's term.

However, officials note that Bush has been a longtime defender of Gonzales, whom he hired as his general counsel in 1994 when he was elected Texas governor.

He may not be willing to give in to congressional demands to remove him, unless he becomes convinced that keeping Gonzales will hinder his agenda, they said.

Sen. John Cornyn, R-Texas, indicated to CNN that he is ambivalent about the possibility that Gonzales might leave.

"If Al Gonzales were to quit tomorrow, it wouldn't end it. It would just, I think, add fuel to the fire, especially with Democrats controlling the Senate," he said.

"We'd have a confirmation hearing with the new attorney general, with a year and half left to serve in President Bush's second term in office. I think it would be more chaotic than it would if he were to stay and try to do the best job he can under very difficult circumstances."